| Summary: | We discuss a general method for constructing nonreciprocal, cavity-based photonic devices, based on matching a given coherent interaction with its corresponding dissipative counterpart; our method generalizes the basic structure used in the theory of cascaded quantum systems and can render an extremely wide class of interactions directional. In contrast to standard interference-based schemes, our approach allows directional behavior over a wide bandwidth. We show how it can be used to devise isolators and directional, quantum-limited amplifiers. We discuss in detail how this general method allows the construction of a directional, noise-free phase-sensitive amplifier that is not limited by any fundamental gain-bandwidth constraint. Our approach is particularly well suited to implementations using superconducting microwave circuits and optomechanical systems.
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